涩里番

Noise-induced pattern formation in networks of spatially-dependent neural networks

Daniele Avitabile,聽VU University Amsterdam
Tuesday February 17, 12-1pm
Zoom Link:听
In Person: 550 Sherbrooke, Room 189

Abstract: This talk presents a study of pattern formation in a class of high-dimensional neural networks defined on random graphs and subjected to spatio-temporal stochastic forcing. The connectivity matrices of these neural networks are randomly generated and can be excitatory or inhibitory, dense or sparse, and need not be symmetric. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting system are the mean and variance of neuronal activity. We select networks with tractable mean-field equations and perform a bifurcation analysis using the diffusivity strength of the afferent white noise on each neuron as the control parameter. We identify conditions for Turing-like bifurcations in a system where the cortex is modeled as a ring and provide numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. We present numerical evidence that solutions of the finite-size network converge weakly to those of the mean-field model. If time permits, I will discuss recent extensions of this work that involve dynamics on the network weights, and the employment of Wilson-Cowan neural field-type equations in data assimilation problems